= Solution
At cryogenic temperatures, the <intrinsic carrier concentration> is exponentially small, while a low phonon population permits relatively sharp band-edge and <exciton> spectral features. Near room temperature, thermal electron–hole generation increases strongly:
$$
n_i=\sqrt{N_cN_v}\,e^{-E_g/(2k_{\mathrm B}T)}.
$$
This generally raises intrinsic conductivity, although increased <phonon> scattering tends to lower the individual carrier mobilities. With a gap of $1.24$ eV, the material remains far from a degenerate metal at room temperature.
For optical structure, compare $k_{\mathrm B}T\simeq25.9$ meV at 300 K with the <exciton binding energies>. The $n=2$ binding of $9.56$ meV is substantially smaller, so excited bound states are readily thermally disrupted and broadened. The ground binding of $38.24$ meV is larger but only about $1.48k_{\mathrm B}T$: the ground exciton need not disappear completely, yet strong thermal ionization and broadening can weaken its sharp line. A comparison with $k_{\mathrm B}T$ is a useful scale argument, not an exact bound-pair fraction independent of density or lifetime.
Thermal lattice expansion and electron–phonon interactions can also shift a real material's gap and optical edge. The given fixed tight-binding parameters contain no temperature dependence, so they do not determine the magnitude or even a universal sign of that extra gap shift. Within the stated model, the dependable trends are more thermally generated carriers and less distinct excitonic structure on warming.
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